To develop UAMP-SBL, we apply structured variational inference (SVI) [1]}, [2]}, [3]}.
In particular, the formulated problem is represented by a factor graph model, based on which approximate inference is implemented in terms of structured variational message passing (SVMP) [2]}, [3]}, [6]}. The use of SVMP allows the incorporation of UAMP to the message passing algorithm to handle the most computational intensive part of message computations with high robustness and low complexity. In UAMP-SBL, a Gamma distribution is used as the hyperprior for the precisions of the elements of \(\mathbf {x}\) . blackWe propose to tune the shape parameter of the Gamma distribution automatically during iterations.
We show by simulations that, in many cases black with a generic measurement matrix, UAMP-SBL can still approach the support-oracle bound closely. We also investigate blackSE-based performance prediction for UAMP-SBL and analyze the impact of the shape parameter on SBL.
In addition, blackthe UAMP-SBL algorithm is extended from single measurement vector (SMV) problems to multiple measurement vector (MMV) problems [7]}, [8]}, [9]}.
Based on our preliminary results in [10]}blackCompared to [10]}, we present a new derivation of UAMP-SBL, extend it from SMV to MMV, and provide theoretical analyses and comprehensive comparisons., UAMP-SBL was applied to inverse synthetic aperture radar (ISAR) [12]}, where the measurement matrix can be highly correlated in order to achieve high Doppler resolution. Real data experiments in [12]} demonstrate its superiority in terms of both recovery performance and speed.
